Package fuzzy :: Package set :: Module operations

Module operations


Helper functions for calculation with fuzzy sets.

Examples can be found here U{http://pyfuzzy.sourceforge.net/demo/merge/}

* Intersection of set1 and set2 can be done by
  
  C{set = merge(T_NORM,set1,set2)}
  
  where T_NORM is a t-norm eg. Min.
  (or a function which accepts two parameters as min().)

* Union of set1 and set2 can be done by
  
  C{set = merge(S_NORM,set1,set2)}
  
  where S_NORM is a s-norm eg. Max.
  (or a function which accepts two parameters as max().)

* Complement of set1 can be done by
  
  C{set = norm(lambda a,b:1.0-a ,set1,0.0)}
  
  using a user defined function for it.
  (The second parameter is ignored or better said
  it doesn't influence the value, it only influences
  maybe where the points of the resulting polygon are
  set.)

* Activation function can be done by
  
  C{set = norm(act_norm,set,act_value)}
  
  where act_norm is any L{fuzzy.norm} or two params function (eg. min)
  and act_value is the result of a rule calculation.

Functions

[hide private]

float

_find_root(f, x1, x2, f1=None, f2=None, epsilon=None)
Find root of function f between x1,x2 by using the regula falsi method with the pegasus modification.

source code

float

_find_root_linear(x1, x2, f1, f2)
Find root x1,x2 by using interpolation.

source code

float

_find_intersection(x1, x2, fa1, fa2, fb1, fb2)
Find intersection of two linear functions fa/fb between x1,x2 with values there fa1/fb1 and fa2/fb2.

source code

check(x, y1, y2)

source code

fuzzy.set.Polygon.Polygon

_merge_generator1(set1, set2)
Returns a new fuzzy set which is the merger of set1 and set2, where the membership of the result set is equal to NORM(set1(x),set2(x)). source code

fuzzy.set.Polygon.Polygon

_merge_generator(NORM, set1, set2)
Returns a new fuzzy set which is the merger of set1 and set2, where the membership of the result set is equal to NORM(set1(x),set2(x)). source code

fuzzy.set.Polygon.Polygon

merge(NORM, set1, set2, segment_size=None)
Returns a new fuzzy set which is the merger of set1 and set2, where the membership of the result set is equal to NORM(set1(x),set2(x)). source code

_norm_generator(NORM, set, value)
Returns a new fuzzy set which is this set normed with value.

source code

fuzzy.set.Polygon.Polygon

norm(NORM, set, value, segment_size=None)
Returns a new fuzzy set which ist this set normed with value.

source code

fuzzy.set.Polygon.Polygon

_complement_generator(COMPLEMENT, set)
Returns a new fuzzy set which is this complement of the given set.

source code

fuzzy.set.Polygon.Polygon

complement(COMPLEMENT, set, segment_size=None)
Returns a new fuzzy set which is this complement of the given set.

source code

Variables

[hide private]

__revision__ = '$Id: operations.py,v 1.13 2013-01-09 20:10:19 ...

__package__ = 'fuzzy.set'

Function Details

[hide private]

_find_root(f, x1, x2, f1=None, f2=None, epsilon=None)

source code

Find root of function f between x1,x2 by using the regula falsi method with the pegasus modification. See also http://de.wikipedia.org/wiki/Regula_Falsi. (The english version lacks the description of pegasus modification.) The algorithm stops if the error estimation is smaller than epsilon or there is an ZeroDivisionError, which means both values f1 and f2 are identical (should be 0 then).

Parameters:

f (f(x)) - function for which to find f(x)=0
x1 (float) - left border of range
x2 (float) - right border of range
f1 (float) - value for x1, if available
f2 (float) - value for x2, if available
epsilon (float/None) - break condition for algorithm (value < epsilon)

Returns: float

x where f(x)=0

_find_root_linear(x1, x2, f1, f2)

source code

Find root x1,x2 by using interpolation.

Parameters:

x1 (float) - left border of range
x2 (float) - right border of range
f1 (float) - value for x1
f2 (float) - value for x2

Returns: float

x where f(x)=0

_find_intersection(x1, x2, fa1, fa2, fb1, fb2)

source code

Find intersection of two linear functions fa/fb between x1,x2 with values there fa1/fb1 and fa2/fb2.

Parameters:

x1 (float) - left border of range
x2 (float) - right border of range
fa1 (float) - value for x1
fa2 (float) - value for x2
fb1 (float) - value for x1
fb2 (float) - value for x2

Returns: float

x where fa(x)-fb(x)=0

_merge_generator1(set1, set2)

source code

Returns a new fuzzy set which is the merger of set1 and set2, where the membership of the result set is equal to NORM(set1(x),set2(x)).

Parameters:

set1 (fuzzy.set.Set) - fuzzy set
set2 (fuzzy.set.Set) - fuzzy set

Returns: fuzzy.set.Polygon.Polygon

resulting fuzzy set

_merge_generator(NORM, set1, set2)

source code

Returns a new fuzzy set which is the merger of set1 and set2, where the membership of the result set is equal to NORM(set1(x),set2(x)).

Parameters:

NORM (fuzzy.norm.Norm.Norm) - fuzzy norm to calculate both sets values. For example Min(), Max(), ... Also possible as two params function, eg. lambda a,b: (a+b)/2..
set1 (fuzzy.set.Set) - fuzzy set
set2 (fuzzy.set.Set) - fuzzy set

Returns: fuzzy.set.Polygon.Polygon

resulting fuzzy set

merge(NORM, set1, set2, segment_size=None)

source code

Returns a new fuzzy set which is the merger of set1 and set2, where the membership of the result set is equal to NORM(set1(x),set2(x)).

For nonlinear operations you might want set the segment size to a value which controls how large a linear segment of the result can be. See also the following examples:

http://pyfuzzy.sourceforge.net/demo/merge/AlgebraicProduct_d_d.png - The algebraic product is x*y, so using it on the same set, it calculates the square of it.
http://pyfuzzy.sourceforge.net/demo/merge/AlgebraicSum_d_d.png - The algebraic sum is x+y-x*y.

Parameters:

NORM (fuzzy.norm.Norm.Norm) - fuzzy norm to calculate both sets values. For example Min(), Max(), ... Also possible as two params function, eg. lambda a,b: (a+b)/2..
set1 (fuzzy.set.Set) - fuzzy set
set2 (fuzzy.set.Set) - fuzzy set
segment_size (float/None) - maximum size of a segment

Returns: fuzzy.set.Polygon.Polygon

resulting fuzzy set

_norm_generator(NORM, set, value)

source code

Returns a new fuzzy set which is this set normed with value. where the membership of the result set is equal to NORM(set(x),value).

Parameters:

NORM (fuzzy.norm.Norm.Norm) - fuzzy norm to calculate set's values with value. For example Min(), Max(), ... Also possible as two params function, eg. lambda a,b: (a+b)/2..
set (fuzzy.set.Set) - fuzzy set
value (float) - value

norm(NORM, set, value, segment_size=None)

source code

Returns a new fuzzy set which ist this set normed with value. where the membership of the result set is equal to NORM(set(x),value).

For meaning of segment_size see also fuzzy.set.operations.merge.

Parameters:

NORM (fuzzy.norm.Norm.Norm) - fuzzy norm to calculate set's values with value. For example Min(), Max(), ... Also possible as two params function, eg. lambda a,b: (a+b)/2..
set (fuzzy.set.Set) - fuzzy set
value (float) - value
segment_size (float/None) - maximum size of a segment

Returns: fuzzy.set.Polygon.Polygon

resulting fuzzy set

_complement_generator(COMPLEMENT, set)

source code

Returns a new fuzzy set which is this complement of the given set. (Where the membership of the result set is equal to COMPLEMENT(set(x)).

Parameters:

COMPLEMENT (fuzzy.complement.Base.Base) - fuzzy complement to use. For example Zadeh(), ... Also possible as one param function, eg. lambda x: 1.-x.
set (fuzzy.set.Set) - fuzzy set

Returns: fuzzy.set.Polygon.Polygon

resulting fuzzy set

complement(COMPLEMENT, set, segment_size=None)

source code

Returns a new fuzzy set which is this complement of the given set. (Where the membership of the result set is equal to COMPLEMENT(set(x)).

For meaning of segment_size see also fuzzy.set.operations.merge.

Parameters:

COMPLEMENT (fuzzy.complement.Base.Base) - fuzzy complement to use. For example Zadeh(), ... Also possible as one param function, eg. lambda x: 1.-x.
set (fuzzy.set.Set) - fuzzy set
segment_size (float/None) - maximum size of a segment

Returns: fuzzy.set.Polygon.Polygon

resulting fuzzy set

Variables Details

[hide private]

revision

Value:

'$Id: operations.py,v 1.13 2013-01-09 20:10:19 rliebscher Exp $'